Title: Secondary bifurcation for a nonlocal Allen-Cahn equation

Speaker:  Professor Shoji Yotsutani, Ryukoku University

Abstract: We study a Neumann problem of a nonlocal Allen-Cahn equation in a finite interval. A main result is a symmetry breaking (secondary) bifurcation on the bifurcation curve of solutions with odd-symmetry. Our proof is based on a level set analysis for the associated integral map. A method using the complete elliptic integrals proves the uniqueness of secondary bifurcation point. We also show results concerning the global bifurcation structure. This is a joint work with K. Kuto, T. Mori, and T. Tsujikawa.